Finite Group Databasebeta

← C2×#20242835 #26198673

Subgroups — C2×#20242835 #26198673

Order 12032.

754 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689471C211yesmaximal, characteristic
2C2×#15689330C211yesmaximal, characteristic, complemented
3C2×#15689324C211yesmaximal, characteristic
4C2×#15689247C211yesmaximal, characteristic, complemented
5#20242835C218yesmaximal, direct product factor
6C2×#15688875C211yesmaximal, characteristic, complemented
7C2×#15688866C211yesmaximal, characteristic
8C2×C47×#332C211yesmaximal, characteristic, complemented
9C22×#10625337—21no—
10C22×#10625325—21no—
11C2×#13094021C2211yescharacteristic
12C2×C4×Dic94C2211yescharacteristic
13#15689471—22no—
14#15689471C2214yes—
15#15689330—22no—
16#15689330C2214yescomplemented
17#15689324—22no—
18#15689324C2214yes—
19#15689247—22no—
20#15689247C2214yescomplemented
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×Dic47⋊C8—21no—
23C2×#13093948—21no—
24C2×#13093946—21no—
25C2×#13093944—21no—
26C2×#13093944—21no—
27C2×C4×C47⋊C8C2211yescharacteristic
28C2×C8×Dic47—21no—
29#15688875C2214yescomplemented
30#15688866C2214yes—
31C2×C4⋊Q8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C47×#332C2214yescomplemented
35C22×Dic94D411yescharacteristic
36C22×D188—21no—
37C22×D188—21no—
38C22×D188—21no—
39C2×#10625337—24no—
40C2×#10625337—44no—
41C2×#10625325—24no—
42C2×#10625325—44no—
43C22×C47⋊C8—21no—
44C22×C47⋊C8D411yescharacteristic
45C22×C47⋊C8D411yescharacteristic
46#13094021—21no—
47#13094021—21no—
48#13094021—21no—
49#13094021C2312yes—
50C4×Dic94—21no—
51C4×Dic94—21no—
52C4×Dic94D412yes—
53C4×Dic94C2312yes—
54C2×C4⋊Dic47D411yescharacteristic
55C2×Dic47⋊C4—21no—
56C2×C4×Dic47—21no—
57C4⋊(C47⋊C8)—21no—
58C4⋊(C47⋊C8)C2312yes—
59Dic47⋊C8—24no—
60#13093948—24no—
61#13093946—24no—
62#13093944—24no—
63#13093944—24no—
64C4×C47⋊C8D412yes—
65C4×C47⋊C8C2312yes—
66C8×Dic47—24no—
67C22×Q8×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C4⋊Q8×C47—21no—
71C4⋊Q8×C47—21no—
72C4⋊Q8×C47—21no—
73C4⋊Q8×C47C2312yes—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C42×C47C2311yescharacteristic
77C4⋊C8×C47—21no—
78C4⋊C8×C47—21no—
79C4⋊C8×C47C2312yes—
80C4⋊C8×C47C2312yes—
81C23×D47—41no—
82C2×Q8×C47—22no—
83C2×Q8×C47—41no—
84C2×Q8×C47—42no—
85C2×Q8×C47—42no—
86C22×C4×C47—41no—
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47#4111yescharacteristic
90C22×Dic47—21no—
91C22×Dic47—21no—
92C2×D188—22no—
93C2×D188—22no—
94C2×D188—22no—
95C2×D188—42no—
96C2×D188—42no—
97C2×D188—42no—
98C2×D188—42no—
99C2×D188—41no—
100C2×D188—41no—
101C2×D188—41no—
102C2×D188—82no—
103C2×Dic94—21no—
104C2×Dic94—22no—
105C2×Dic94D814yes—
106C2×Dic94C2×D412yes—
107C2×C8×C47—22no—
108C2×C8×C47—22no—
109C2×C8×C47—42no—
110C2×C8×C47—42no—
111C4⋊C4×C47—22no—
112C4⋊C4×C47—22no—
113C4⋊C4×C47—41no—
114C4⋊C4×C47—41no—
115C42×C47C2×D411yescharacteristic
116C42×C47C2×D411yescharacteristic
117C42×C47#4111yescharacteristic
118C42×C47C2411yescharacteristic
119#10625337—48no—
120C4⋊Dic47—21no—
121C4⋊Dic47C2×D412yes—
122Dic47⋊C4—22no—
123Dic47⋊C4—22no—
124C4×Dic47—22no—
125C4×Dic47—22no—
126C2×C47⋊C8—22no—
127C2×C47⋊C8—22no—
128C2×C47⋊C8—22no—
129C2×C47⋊C8—42no—
130C2×C47⋊C8C2×D412yes—
131C2×C47⋊C8C2×D412yes—
132#10625325—48no—
133C23×C47#12111yescharacteristic
134C22×D47—42no—
135C22×D47—82no—
136C22×D47—82no—
137C22×D47—82no—
138Q8×C47—42no—
139Q8×C47—42no—
140Q8×C47—82no—
141C2×C4×C47—22no—
142C2×C4×C47—42no—
143C2×C4×C47—82no—
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47C2×D812yes—
148C2×C4×C47#13512yes—
149C2×C4×C47#13512yes—
150C2×C4×C47#13712yes—
151C2×C4×C47C22×D411yescharacteristic
152C2×C4×C47C22×D411yescharacteristic
153C2×C4×C47C2×#4111yescharacteristic
154C2×Dic47—22no—
155C2×Dic47—24no—
156C2×Dic47—22no—
157C2×Dic47—42no—
158D188—42no—
159D188—42no—
160D188—42no—
161D188—42no—
162D188—82no—
163D188—82no—
164D188—82no—
165D188—82no—
166Dic94—22no—
167Dic94—24no—
168Dic94C2×D814yes—
169C8×C47—42no—
170C8×C47—42no—
171C47⋊C8—22no—
172C47⋊C8—22no—
173C47⋊C8—42no—
174C2×#1682—471nomaximal, Sylow
175C22×C47#46412yes—
176C22×C47#46612yes—
177C22×C47#47112yes—
178C22×C47C2×#12111yescharacteristic
179C2×D47—82no—
180C2×D47—82no—
181C2×D47—82no—
182C2×D47—164no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—82no—
186C4×C47#46412yes—
187C4×C47#46612yes—
188C4×C47C22×D811yescharacteristic
189C4×C47C2×#13511yescharacteristic
190C4×C47C2×#13511yescharacteristic
191C4×C47C2×#13711yescharacteristic
192Dic47—24no—
193Dic47—42no—
194C2×#486—471no—
195C2×#462—471no—
196C2×#460—471no—
197C2×C8×Q8—471no—
198#1682—478no—
199C2×#335—471no—
200C2×#332D4711yescharacteristic, complemented
201C2×#331—471no—
202C2×C47#168214yescomplemented
203C2×C47C2×#46411yescharacteristic
204C2×C47C2×#46611yescharacteristic
205C2×C47C2×#47111yescharacteristic
206D47—162no—
207C22×Q16—941no—
208C22×SD16—941no—
209C2×C4⋊Q8C2×D4711yescharacteristic
210C2×#127—471no—
211C2×C4×Q8—471no—
212#486—474no—
213#486—942no—
214#462—474no—
215#462—942no—
216#460—474no—
217#460—942no—
218C8×Q8—474no—
219C8×Q8—942no—
220C2×C4⋊C8—471no—
221C2×C4⋊C8—941no—
222C2×C4⋊C8C2×D4711yescharacteristic
223C2×C4⋊C8C2×D4711yescharacteristic
224C2×#103—941no—
225C2×#102—941no—
226C2×#102—941no—
227C2×#102—941no—
228C2×C4×C8—471no—
229C2×C4×C8—941no—
230#335—474no—
231#332C2×D4714yescomplemented
232#331—474no—
233C47C2×#168211yescharacteristic, complemented, Sylow
234C22×Q8—21no—
235C22×Q8—471no—
236C22×D4—941no—
237C22×D4—941no—
238C22×D4—941no—
239C2×Q16—944no—
240C2×Q16—1884no—
241C2×SD16—944no—
242C2×SD16—1884no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—471no—
246C22×C8—471no—
247C22×C8—941no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C22×D4712yes—
252#127—472no—
253#127—941no—
254#127—941no—
255#127—941no—
256C4×Q8—472no—
257C4×Q8—472no—
258C4×Q8—941no—
259C4×Q8—941no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—471no—
263C2×C4⋊C4—941no—
264C2×C42—941no—
265C2×C42C22×D4711yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—472no—
269C4⋊C8—944no—
270C4⋊C8—941no—
271C4⋊C8C22×D4712yes—
272C4⋊C8C22×D4712yes—
273#103—944no—
274#102—944no—
275#102—944no—
276#102—944no—
277C4×C8—472no—
278C4×C8—472no—
279C4×C8—944no—
280C24—1881no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—474no—
286C2×Q8—472no—
287C2×Q8—941no—
288C2×Q8—942no—
289C2×D4—942no—
290C2×D4—942no—
291C2×D4—942no—
292C2×D4—3762no—
293C2×D4—1881no—
294C2×D4—1881no—
295C2×D4—1881no—
296C2×D4—1882no—
297C2×D4—1882no—
298C2×D4—1882no—
299C2×D4—1882no—
300C22×C4—41no—
301C22×C4—941no—
302C22×C4—941no—
303C22×C4#1062535011yescharacteristic
304C22×C4D4×D4711yescharacteristic
305C22×C4D4×D4711yescharacteristic
306Q16—1888no—
307SD16—1888no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—472no—
313C2×C8—472no—
314C2×C8—942no—
315C2×C8—942no—
316C2×C8—942no—
317C2×C8—1882no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—472no—
323C4⋊C4—942no—
324C4⋊C4—941no—
325C4⋊C4—942no—
326C42—942no—
327C42—942no—
328C42#1062535011yescharacteristic
329C42D4×D4711yescharacteristic
330C42D4×D4711yescharacteristic
331C42C23×D4711yescharacteristic
332C23—3762no—
333C23—3762no—
334C23—3762no—
335C23—1882no—
336C23#1309399711yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—474no—
341Q8—944no—
342Q8—942no—
343D4—3762no—
344D4—3762no—
345D4—3762no—
346D4—3762no—
347D4—1882no—
348D4—1882no—
349D4—1882no—
350D4—1882no—
351C2×C4—22no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—944no—
355C2×C4—942no—
356C2×C4—942no—
357C2×C4—1882no—
358C2×C4#1309399711yescharacteristic
359C2×C4#1309399711yescharacteristic
360C2×C4#1309399711yescharacteristic
361C2×C4D8×D4712yes—
362C2×C4#1309404512yes—
363C2×C4#1309404512yes—
364C2×C4#1309405612yes—
365C2×C4C2×D4×D4711yescharacteristic
366C2×C4C2×D4×D4711yescharacteristic
367C2×C4C2×#1062535011yescharacteristic
368C8—42no—
369C8—42no—
370C8—942no—
371C8—942no—
372C8—1882no—
373C22—3762no—
374C22—3762no—
375C22—3762no—
376C22—7524no—
377C22#1568934812yes—
378C22#1568935812yes—
379C22#1568938912yes—
380C22C2×#1309399711yescharacteristic
381C4—21no—
382C4—21no—
383C4—82no—
384C4—944no—
385C4—1882no—
386C4#1568934812yes—
387C4#1568935812yes—
388C4C2×D8×D4711yescharacteristic
389C4C2×#1309404511yescharacteristic
390C4C2×#1309404511yescharacteristic
391C4C2×#1309405611yescharacteristic
392C2—7522no—
393C2#2024283514yesdirect product factor
394C2C2×#1568934811yescharacteristic
395C2C2×#1568935811yescharacteristic
396C2C2×#1568938911yescharacteristic
subgroupG/H
centerC23#13093997
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#332C2
socleC23×C47#121
prime radicalC2×#13094021C22
hypercenterC2×#332D47
hypocenterC47C2×#1682
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#15689330C2semidirect
4. C2×#15689247C2semidirect
5. #20242835C2direct (N × H)
6. C2×#15688875C2semidirect
8. C2×C47×#332C2semidirect
16. #15689330C22semidirect
20. #15689247C22semidirect
29. #15688875C22semidirect
34. C47×#332C22semidirect
200. C2×#332D47semidirect
202. C2×C47#1682semidirect
231. #332C2×D47semidirect
233. C47C2×#1682semidirect
393. C2#20242835direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156894712
C2×#156893302
C2×#156893242
C2×#156892472
#202428352
C2×#156888752
C2×#156888662
C2×C47×#3322
C2×#168247